all pass filter design

How do I derive the coefficients for a All pass Filter transfer function? I tried deriving the Delay and tried putting its derivatives to 0 at w=0 for the 1st order All pass filter but could not get anywhere.

"Coefficient for 1st order allpass filter? (an answer)"
http://music.calarts.edu/pipermail/m...er/002227.html

Regards,
IanP

This seems like a formula for a discrete filter. I wanted to know about a Analog filter, in the opamps for everyone TI handbook they give the coefficient tables but they give no hint as to how to derive them.

The placement depends on the response you want. For constant time delay with frequency, the poles are those of flat delay filters (Gaussian or Thompson) with mirror image zeros.

Is there any place I can see how their (gaussian and thompson)coefficients are derived. I have attached the filter table showing the coefficients for the 1st and 2nd order All pass filter, these are the ones I am looking to derive.
fc =1 in this and fi is the frequency at which the phase becomes 180 degrees